This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A376789 #12 Oct 16 2024 21:36:28
%S A376789 1,1,0,2,1,0,3,1,0,0,6,1,1,0,0,9,2,2,1,0,0,18,2,4,1,0,0,0,30,4,7,1,0,
%T A376789 1,0,0,56,5,14,1,1,1,0,0,0,99,8,25,2,1,2,1,0,0,0,186,11,48,2,2,3,2,1,
%U A376789 0,0,0,335,18,88,3,3,6,4,1,0,0,0,0
%N A376789 Table read by antidiagonals: T(n,k) is the number of Lyndon words of length k on the alphabet {0,1} whose prefix is the bitwise complement of the binary expansion of n with n >= 1 and k >= 1.
%C A376789 T(n,k) = 0 if n is in A366195.
%C A376789 Row 1 is A059966.
%C A376789 Row 2 is A006206 for n > 1.
%C A376789 Row 3 is A065491 for n > 2.
%C A376789 Row 4 is A065417.
%C A376789 Row 6 is A349904.
%e A376789 Table begins
%e A376789 n\k| 1 2 3 4 5 6 7 8 9 10 11 12
%e A376789 ---+-------------------------------------------
%e A376789 1 | 1, 1, 2, 3, 6, 9, 18, 30, 56, 99, 186, 335
%e A376789 2 | 0, 1, 1, 1, 2, 2, 4, 5, 8, 11, 18, 25
%e A376789 3 | 0, 0, 1, 2, 4, 7, 14, 25, 48, 88, 168, 310
%e A376789 4 | 0, 0, 1, 1, 1, 1, 2, 2, 3, 4, 6, 7
%e A376789 5 | 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 12, 18
%e A376789 6 | 0, 0, 1, 1, 2, 3, 6, 10, 18, 31, 56, 96
%e A376789 7 | 0, 0, 0, 1, 2, 4, 8, 15, 30, 57, 112, 214
%e A376789 8 | 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 3
%e A376789 9 | 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 3, 4
%e A376789 10 | 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 12, 18
%e A376789 11 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
%e A376789 12 | 0, 0, 0, 1, 1, 2, 3, 5, 9, 15, 26, 43
%e A376789 T(6,5) = 2 because 6 is 110 in base 2, its bitwise complement is 001, and there are T(6,5) = 2 length-5 Lyndon words that begin with 001: 00101 and 00111.
%Y A376789 Cf. A059966, A006206, A065491, A065417, A349904.
%Y A376789 Cf. A365746.
%K A376789 nonn,base,tabl
%O A376789 1,4
%A A376789 _Peter Kagey_, Oct 04 2024